Sampling theorem associated with the discrete cosine transform

Jelena Kovacevic, Markus Püschel

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

One way of deriving the discrete Fourier transform (DFT) is by equispaced sampling of periodic signals or signals on a circle. In this paper, we show that an analogous derivation can be used to obtain the DCT (type 2). To achieve this goal, we replace the circle by a line graph with symmetric boundary conditions, and define signal space, filter space, and filtering operation appropriately. Further, we derive the corresponding sampling theorem including the proper notions of "bandlimited" and "sinc function." The results show that, in a rigorous sense, the DCT is closely related to the DFT, and can be introduced without concepts from statistical signal processing as is the current practice.

Original languageEnglish (US)
Title of host publication2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings
Volume3
StatePublished - Dec 1 2006
Event2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006 - Toulouse, France
Duration: May 14 2006May 19 2006

Other

Other2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006
CountryFrance
CityToulouse
Period5/14/065/19/06

Fingerprint

discrete cosine transform
Discrete cosine transforms
Discrete Fourier transforms
theorems
sampling
Sampling
Signal processing
Boundary conditions
signal processing
derivation
boundary conditions
filters

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing
  • Acoustics and Ultrasonics

Cite this

Kovacevic, J., & Püschel, M. (2006). Sampling theorem associated with the discrete cosine transform. In 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings (Vol. 3). [1660664]

Sampling theorem associated with the discrete cosine transform. / Kovacevic, Jelena; Püschel, Markus.

2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings. Vol. 3 2006. 1660664.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kovacevic, J & Püschel, M 2006, Sampling theorem associated with the discrete cosine transform. in 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings. vol. 3, 1660664, 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006, Toulouse, France, 5/14/06.
Kovacevic J, Püschel M. Sampling theorem associated with the discrete cosine transform. In 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings. Vol. 3. 2006. 1660664
Kovacevic, Jelena ; Püschel, Markus. / Sampling theorem associated with the discrete cosine transform. 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings. Vol. 3 2006.
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